m∠11 = 128°.
A line that cuts three parallel lines forms congruent angles which means they measure the same.
In this problem m∠1 = 52° = m∠4 = m∠5 = m∠8 = m∠9 = m∠12, and m∠2 = m∠3 = m∠6 = m∠7 = m∠10 = m∠11.
To calculate m∠11, we know that m∠12 = m∠1 = 52°, the sum of the angle of m∠11 and m∠12 is 180°. Then:
m∠11 + m∠12 = 180°, with m∠1 = 52° = m∠12
m∠11 + 52° = 180°
m∠11 = 180° - 52°
m∠11 = 128°
